Question: Given $ m \angle ABC = 6x - 33$, $ m \angle CBD = 2x + 8$, and $ m \angle ABD = 47$, find $m\angle ABC$. $B$ $A$ $D$ $C$
Explanation: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Substitute in the expressions that were given for each measure: $ {6x - 33} + {2x + 8} = {47}$ Combine like terms: $ 8x - 25 = 47$ Add $25$ to both sides: $ 8x = 72$ Divide both sides by $8$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 6({9}) - 33$ Simplify: $ {m\angle ABC = 54 - 33}$ So ${m\angle ABC = 21}$.